A mixed integer programming approach to minibeam aperture optimization for multi‐collimator proton minibeam radiotherapy - Shinde, Nimita; Zhang, Weijie; Lin, Yuting; Gao, Hao (Medical physics (Lancaster), 2025)
Background Multi‐collimator proton minibeam radiation therapy (MC‐pMBRT) has recently emerged as a versatile technique for dose shaping, enabling the formation of peak‐valley dose patterns in organs‐at‐risk (OAR) while maintaining a uniform dose distribution in tumor targets. MC‐pMBRT leverages a set of generic multi‐slit collimators (MSCs), each with different center‐to‐center (ctc) distances. However, the current method for minibeam aperture optimization (MAO), that is, the selection of MSC per beam angle to optimize plan quality, is manual and heuristic, resulting in computational inefficiencies and no guarantee of optimality. Purpose This work introduces a novel mixed integer programming (MIP) approach to MAO for optimizing MC‐pMBRT plan quality. Methods The proposed MIP approach jointly optimizes dose distributions and peak‐to‐valley dose ratio (PVDR) and selects the optimal set of MSC per beam angle. The optimization problem includes decision variables for MSC selection per beam angle and spot weights. The proposed MIP approach is a two‐step process: in the first step, the values of binary variables are determined to select MSC for each beam angle; in the second step, the continuous variables are solved to determine the spot weights. Both steps utilize iterative convex relaxation (ICR) and the alternating direction method of multipliers (ADMM) to solve the optimization problems efficiently. Results The proposed MIP method to solve MAO (MIP‐MAO) was validated against the conventional heuristic method (CONV) for MC‐pMBRT treatment planning. Results indicate that MIP‐MAO enhances the conformity index (CI) for the target and improves PVDR for OAR. For instance, in a head‐and‐neck (HN) case, CI improved from 0.61 (CONV) to 0.70 (MIP‐MAO); in an abdomen case, CI improved from 0.78 (CONV) to 0.83 (MIP‐MAO). Additionally, MIP‐MAO reduced mean doses in the body and OAR. Conclusions A novel MIP approach for MAO in MC‐pMBRT is presented, showing demonstrated improvements in plan quality and PVDR compared to the heuristic method.